CN112991196B - Frequency domain denoising method for rotary kiln flame image - Google Patents
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Abstract
The invention provides a frequency domain denoising method for a flame image of a rotary kiln, which fully combines the multi-scale characteristic of image wavelets and the characteristic of non-local mean filtering utilizing image redundant information, utilizes the image wavelets to decompose and filter noise of a high frequency band, and utilizes low frequency information to restore the image, thereby realizing the functions of effectively removing the flame image noise in the frequency domain and well retaining flame detail information. The method reasonably utilizes the distribution characteristics of flame image information and noise in the frequency domain, utilizes the multi-scale characteristics of the image wavelet technology to denoise the flame image in the frequency domain, and has higher efficiency compared with the traditional method. The invention combines the image wavelet transform with the non-local mean de-noising algorithm to carry out non-local mean filtering on the wavelet decomposition coefficients of the two-level and three-level images, thereby realizing better visual perception quality. The invention is suitable for different noise intensities and has good visual quality.
Description
Technical Field
The invention belongs to the technical field of digital image frequency domain denoising, and particularly relates to a frequency domain denoising method for a flame image of a rotary kiln.
Background
The thermal equipment used for calcining cement clinker is called rotary kiln, its main function is to sinter raw slurry into qualified clinker, and its operation condition directly determines the quality of cement clinker. The firing zone flame image contains rich firing zone temperature field information and clinker sintering condition information, and the firing zone temperature field information and the clinker sintering condition information are main references for identifying the firing state together with process data information. However, under the influence of the coal dust and the smoke dust in the kiln, strong coupling exists between the interested areas in the flame image of the burning zone, the boundary is fuzzy, in addition, the process data contains a large amount of complex noise, and the accuracy of the conventional burning state identification technology based on image segmentation or process variables and the method for soft measurement of clinker quality indexes is not high. Therefore, the method and the device for denoising the flame image of the rotary kiln in the frequency domain have great significance.
Disclosure of Invention
The technical problem to be solved by the invention is as follows: the method is used for effectively removing the flame image noise in the frequency domain and well retaining the flame detail information.
The technical scheme adopted by the invention for solving the technical problems is as follows: a frequency domain denoising method for a rotary kiln flame image comprises the following steps:
s1: constructing a weighted adjacency matrix W for the rotary kiln flame image I by utilizing image similarity;
s2: obtaining a graph Laplace matrix L according to the adjacency matrix structure W in the step S1;
s3: performing first-level map wavelet decomposition on the rotary kiln flame image I and obtaining a low-frequency coefficient and a high-frequency coefficient by adopting Chebyshev polynomial approximation;
s4: performing second-level image wavelet decomposition on the first-level image wavelet decomposition obtained first-level image wavelet high-frequency coefficient to obtain second-level decomposed low-frequency and high-frequency coefficients;
s5: performing third-level image wavelet decomposition on the first scale high-frequency coefficient obtained after the second-level image wavelet decomposition to obtain a low-frequency coefficient and a high-frequency coefficient after the third-level decomposition;
s6: performing non-local mean filtering processing on the low-frequency coefficients obtained in the step S4 and the step S5;
s7: and integrating a low-frequency coefficient obtained after the wavelet decomposition of the three-level image, and performing inverse image wavelet transformation to obtain a denoised flame image of the rotary kiln.
According to the scheme, in the step S1, the specific steps are as follows: converting a signal of a flame image I of the rotary kiln into an undirected connected and weighted graph signal G which is { V, epsilon, W }, wherein V is a group of vertexes, epsilon is a group of edges, W is a weighted adjacency matrix, and the dimension of W is Q multiplied by Q, wherein Q is mxn, and the flame image I of the rotary kiln is mxn; let the pixel value of the image block centered on the pixel point i be
The pixel value of the image block with the pixel point j as the center is
The dimension is p multiplied by p, and p is a positive integer; let the horizontal and vertical coordinates of the central pixel of the image block i be l i The horizontal and vertical coordinates of the central pixel point of the image block j are l j (ii) a Setting the influence index for controlling the similarity of the image block as eta, the scaling index for controlling the overall similarity as theta, and the distance parameter as k i The nearest k neighbor is dist (i, j) less than or equal to k, and the edge between the pixel point i and the pixel point j is defined by a threshold Gaussian kernel weight functionWeights, then neighbor matrix W i,j Comprises the following steps:
further, in step S2, the specific steps include: an adjacent matrix W constructed in the formula (1) i,j W, the degree matrix corresponding to the adjacent matrix W is D, and the constructed adjacent matrix W is used i,j The laplacian matrix L is constructed as:
L:＝D-W (2)，
the diagonal elements of the degree matrix D are the rows corresponding to the adjacency matrix W and are:
further, in step S3, the specific steps include: performing first-level image wavelet decomposition on the rotary kiln flame image I and obtaining a coefficient matrix A of wavelets by Chebyshev polynomial approximation, wherein the dimension is Q 2 And (J +1), wherein the scale degree of the wavelet decomposition of the graph is J, the first column of the coefficient matrix A is a low-frequency coefficient, and the rest J columns are high-frequency coefficients with corresponding scales respectively.
Further, in step S4, the specific steps include: a first scale high frequency coefficient A [2 ] obtained by wavelet decomposition of the first level graph]∈R Q×1 Constructing an image matrix with m × n dimensions, and performing second-level image wavelet decomposition on the image to obtain a coefficient matrix B of second-level image wavelet transform with a dimension Q 2 And (J +1), wherein the scale degree of the wavelet decomposition of the graph is J, the first column of the coefficient matrix B is a low-frequency coefficient, and the rest J columns are high-frequency coefficients with corresponding scales respectively.
Further, in step S5, the specific steps include: the first scale high frequency coefficient B2 obtained by wavelet decomposition of the second level image]∈R Q×1 Constructing an image matrix with m × n dimensions, and performing a third-level image wavelet decomposition on the image to obtain a coefficient matrix C of the third-level image wavelet transform, wherein the dimension is Q 2 X (J +1), graph waveletThe decomposed scale number is J, the first column of the coefficient matrix C is a low-frequency coefficient, and the rest J columns are high-frequency coefficients of corresponding scales respectively.
Further, in step S6, the specific steps include:
s61: low-frequency coefficient B [1 ] obtained by wavelet decomposition of second-level image]∈R Q×1 And low-frequency coefficient C1 obtained by wavelet decomposition of third-level graph]∈R Q×1 Respectively reconstructed into m × n dimensional matrix B 0 [1]∈R m×n And C 0 [1]∈R m×n ；
S62: for matrix B 0 [1]∈R m×n And C 0 [1]∈R m×n And (3) carrying out non-local mean filtering: in wavelet coefficient matrix B 0 [1]∈R m×n And C 0 [1]∈R m×n Selecting a point i, establishing a D multiplied by D noise search frame Z by taking the selected point i as a center, and taking a neighborhood frame with the size of D multiplied by D in the selected search frame, wherein a neighborhood window slides in a search window; let the neighborhood vector composed of all wavelet coefficients in the neighborhood frame with the pixel point i as the center be v i And the neighborhood vector formed by all wavelet coefficients in the neighborhood frame with the pixel point j as the center is v j If the smoothing parameter is h, the similarity between two neighborhood windows is calculated to obtain the weight value U of the point j to the point i i,j Comprises the following steps:
further, in step S7, the specific steps include:
s71: reconstructing the dimension of the coefficient matrix subjected to the non-local mean filtering obtained in the step S6 to obtain a coefficient vector Bnlm [1 ] consistent with the Chebyshev polynomial approximation dimension]∈R Q×1 And Cnlm [1 ]]∈R Q×1 ；
S72: three low-frequency coefficients obtained by wavelet decomposition of the three-level graph are reconstructed:
Y[1]＝A[1] (5)，
Y[2]＝B nlm [1] (6)，
Y[3]＝C nlm [1] (7)，
obtaining a coefficient matrix Y ∈ R Q×(j+1) ：
Y[i]＝0∈R Q×1 (i＞3) (8)，
Setting the operator matrix as G, and performing inverse transformation on the image wavelet coefficient Y to obtain a denoised rotary kiln flame image P as follows:
(G * G)P＝G * Y (9)。
a computer storage medium having stored therein a computer program executable by a computer processor, the computer program implementing a method for frequency domain denoising of a rotary kiln flame image.
The invention has the beneficial effects that:
1. according to the method for denoising the flame image of the rotary kiln in the frequency domain, disclosed by the invention, the image wavelet decomposition is utilized for filtering the noise of a high frequency band, the image is restored by utilizing the low frequency information, and the functions of effectively removing the noise of the flame image in the frequency domain and better retaining the detail information of the flame are realized.
2. The invention fully combines the multi-scale characteristic of image wavelet and the characteristic of non-local mean filtering utilizing image redundant information, thereby not only realizing better denoising effect, but also keeping the detail information of flame image as far as possible.
3. The method reasonably utilizes the distribution characteristics of flame image information and noise in a frequency domain, utilizes the multi-scale characteristics of the image wavelet technology, denoises the flame image in a frequency domain, and has higher efficiency compared with the traditional method.
4. The invention combines the image wavelet transform with the non-local mean de-noising algorithm, carries out non-local mean filtering on the wavelet decomposition coefficients of the two-level and three-level images, reasonably utilizes the redundant information of the images, reserves more structural information and details of the flame images and realizes better visual perception quality.
5. The invention has the characteristics of organically combining the denoising performance and the detail retention and being suitable for different noise intensities and good visual quality.
Drawings
FIG. 1 is a flow chart of an embodiment of the present invention.
Fig. 2 is a noisy flame image 1 of an embodiment of the invention.
FIG. 3 is a filtered flame image 1 of an embodiment of the invention.
Fig. 4 is a noisy flame image 2 of an embodiment of the invention.
FIG. 5 is a filtered flame image 2 of an embodiment of the invention.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings and specific embodiments.
Referring to fig. 1, a frequency domain denoising method for a flame image of a rotary kiln according to an embodiment of the present invention includes the following steps:
s1: constructing a weighted adjacency matrix W for the flame image I of the rotary kiln by utilizing image similarity, and specifically comprising the following steps: converting the signal of the rotary kiln flame image I into an undirected connected and weighted graph signal G ═ V, epsilon, W }, wherein V is a group of vertexes, epsilon is a group of edges, W is a weighted adjacency matrix, and the dimension of W is 101376 multiplied by 101376, wherein 101376 is 288 multiplied by 352, and the rotary kiln flame image I is 288 multiplied by 352; let the pixel value of the image block centered on the pixel point i be
The pixel value of the image block with the pixel point j as the center is
The dimension is 5 multiplied by 5; let the horizontal and vertical coordinates of the central pixel of the image block i be l i The horizontal and vertical coordinates of the central pixel point of the image block j are l j (ii) a Let η be 0.001 for the influence indicator controlling the similarity of the image block, θ be 20 for the scaling indicator controlling the overall similarity, and distance parameter 11 for the image block x i The nearest k neighbor of (i, j) is dist (i, j) is less than or equal to 11, the edge weight between the pixel point i and the pixel point j is defined by the threshold Gaussian kernel weight function, and then the adjacent matrix W i,j Comprises the following steps:
s2: obtaining a graph laplacian matrix L according to the adjacency matrix structure W in step S1, specifically including the steps of: an adjacent matrix W constructed in the formula (1) i,j W, the degree matrix corresponding to the adjacent matrix W is D, and the constructed adjacent matrix W is used i,j The laplacian matrix L is constructed as:
L:＝D-W (2)，
the diagonal elements of the degree matrix D are the rows corresponding to the adjacency matrix W and are:
s3: performing first-level map wavelet decomposition on a rotary kiln flame image I and obtaining a low-frequency coefficient and a high-frequency coefficient by adopting Chebyshev polynomial approximation, wherein the method specifically comprises the following steps: performing first-level image wavelet decomposition on the rotary kiln flame image I and obtaining a coefficient matrix A of wavelets by Chebyshev polynomial approximation, wherein the dimension is Q 2 X (4+1), the scale of the wavelet decomposition of the graph is 4, the first column of the coefficient matrix a is a low-frequency coefficient, and the remaining 4 columns are high-frequency coefficients of corresponding scales respectively.
S4: performing second-level image wavelet decomposition on the first-level image wavelet decomposition to obtain low-frequency and high-frequency coefficients after the second-level decomposition, and specifically comprising the following steps of: a first scale high frequency coefficient A [2 ] obtained by wavelet decomposition of the first level graph]∈R 101376×1 Constructing 288 x 352 dimensional image matrix, then carrying out second-level image wavelet decomposition on the image to obtain a coefficient matrix B of second-level image wavelet transform, wherein the dimension is 101376 2 X (4+1), the scale of the wavelet decomposition of the graph is 4, the first column of the coefficient matrix B is a low-frequency coefficient, and the remaining 4 columns are high-frequency coefficients of corresponding scales respectively.
S5: performing third-level image wavelet decomposition on the first scale high-frequency coefficient obtained after the second-level image wavelet decomposition to obtain a low-frequency coefficient and a high-frequency coefficient after the third-level decomposition, and specifically comprising the following steps: the first scale high frequency coefficient B2 obtained by wavelet decomposition of the second level image]∈R 101376×1 Is constructed as 288 x 352-dimensional image matrix, and performing wavelet decomposition on the image to obtain coefficient matrix C of wavelet transform of the third level image, wherein the dimension is 101376 2 (4+1), the scale degree of the wavelet decomposition of the graph is 4, the first column of the coefficient matrix C is a low-frequency coefficient, and the other 4 columns are high-frequency coefficients with corresponding scales respectively.
S6: and (3) performing non-local mean filtering processing on the low-frequency coefficients obtained in the step (S4) and the step (S5), wherein the specific steps are as follows:
s61: low-frequency coefficient B [1 ] obtained by wavelet decomposition of second-level image]∈R 101376×1 And low-frequency coefficient C1 obtained by wavelet decomposition of third-level graph]∈R 101376×1 Respectively reconstructed into 288 x 352 dimensional matrix B 0 [1]∈R 288×352 And C 0 [1]∈R 288 ×352 ；
S62: for matrix B 0 [1]∈R 288×352 And C 0 [1]∈R 288×352 And (3) carrying out non-local mean filtering: in wavelet coefficient matrix B 0 [1]∈R 288×352 And C 0 [1]∈R 288×352 Selecting a point i, establishing a 7 x 7 noise search frame Z by taking the selected point i as a center, taking a neighborhood frame with the size of 3 x 3 in the selected search frame, and sliding a neighborhood window in the search window; let the neighborhood vector composed of all wavelet coefficients in the neighborhood frame with the pixel point i as the center be v i And the neighborhood vector formed by all wavelet coefficients in the neighborhood frame taking the pixel point j as the center is v j If the smoothing parameter is h, the similarity between two neighborhood windows is calculated to obtain the weight value U of the point j to the point i i,j Comprises the following steps:
s7: integrating a low-frequency coefficient obtained after wavelet decomposition of a three-level image, and performing inverse image wavelet transformation to obtain a denoised flame image of the rotary kiln, wherein the specific steps are as follows:
s71: reconstructing the dimensionality of the coefficient matrix subjected to the non-local mean filtering and obtained in the step S6 to obtain the coefficient matrix which is consistent with the Chebyshev polynomial approximation dimensionalityCoefficient vector Bnlm [1 ]]∈R 101376×1 And Cnlm [1 ]]∈R 101376×1 ；
S72: three low-frequency coefficients obtained by wavelet decomposition of the three-level graph are reconstructed:
Y[1]＝A[1] (5)，
Y[2]＝B nlm [1] (6)，
Y[3]＝C nlm [1] (7)，
obtaining a coefficient matrix Y ∈ R 101376×(4+1) ：
Y[i]＝0∈R 101376×1 (i＞3) (8)，
Setting the operator matrix as G, and performing inverse transformation on the image wavelet coefficient Y to obtain a denoised rotary kiln flame image P as follows:
(G * G)P＝G * Y (9)。
referring to fig. 2 to 5, most of energy based on flame image signals is concentrated in a low frequency band of a map domain, and noise is mainly concentrated in a high frequency band. Decomposing the original noisy flame image into low-frequency and high-frequency parts through first image wavelet decomposition; then, carrying out second-time image wavelet decomposition on the first scale of the high-frequency part to obtain high-frequency and low-frequency coefficients after second-time decomposition; then, carrying out image wavelet decomposition on the first scale of the high-frequency signal subjected to the second decomposition to obtain high-frequency and low-frequency coefficients subjected to the third-level decomposition; then, carrying out non-local mean filtering on the low-frequency coefficients obtained after the second-stage and third-stage decomposition; and finally, carrying out inverse image wavelet transform by using a low-frequency coefficient obtained by wavelet decomposition of the three-level image to obtain a denoised flame image of the rotary kiln.
The above embodiments are only used for illustrating the design idea and features of the present invention, and the purpose of the present invention is to enable those skilled in the art to understand the content of the present invention and implement the present invention accordingly, and the protection scope of the present invention is not limited to the above embodiments. Therefore, all equivalent changes or modifications based on the principles and design concepts disclosed herein are intended to be included within the scope of the present invention.
Claims (9)
1. A frequency domain denoising method for a rotary kiln flame image is characterized by comprising the following steps: the method comprises the following steps:
s1: constructing a weighted adjacency matrix W for the rotary kiln flame image I by utilizing image similarity;
s2: obtaining a graph laplacian matrix L according to the adjacency matrix structure W in the step S1;
s3: performing first-level map wavelet decomposition on the rotary kiln flame image I and obtaining a low-frequency coefficient and a high-frequency coefficient by adopting Chebyshev polynomial approximation;
s4: performing second-level image wavelet decomposition on the first-level image wavelet decomposition obtained first-level image wavelet high-frequency coefficient to obtain second-level decomposed low-frequency and high-frequency coefficients;
s5: performing third-level image wavelet decomposition on the first scale high-frequency coefficient obtained after the second-level image wavelet decomposition to obtain a low-frequency coefficient and a high-frequency coefficient after the third-level decomposition;
s6: performing non-local mean filtering processing on the low-frequency coefficients obtained in the step S4 and the step S5;
s7: and integrating a low-frequency coefficient obtained after the wavelet decomposition of the three-level image, and performing inverse image wavelet transformation to obtain a denoised flame image of the rotary kiln.
2. The frequency domain denoising method for the flame image of the rotary kiln as claimed in claim 1, wherein: in the step S1, the specific steps are as follows: converting a signal of a rotary kiln flame image I into an undirected connected and weighted graph signal G ═ V, epsilon, W }, wherein V is a group of vertexes, epsilon is a group of edges, W is a weighted adjacency matrix, and the dimension of W is Q multiplied by Q, wherein Q ═ m multiplied by n, and the rotary kiln flame image I is m multiplied by n dimension; let the pixel value of the image block centered on the pixel point i be
The pixel value of the image block with the pixel point j as the center is
The dimension is p multiplied by p, and p is a positive integer; let the horizontal and vertical coordinates of the central pixel of the image block i be l i The horizontal and vertical coordinates of the central pixel point of the image block j are l j (ii) a Setting the influence index for controlling the similarity of the image block as eta, the scaling index for controlling the overall similarity as theta, and the distance parameter as k i The nearest k neighbor of (a) is that dist (i, j) is less than or equal to k, the edge weight between the pixel point i and the pixel point j is defined by a threshold Gaussian kernel weight function, and then the adjacent matrix W i,j Comprises the following steps:
3. the frequency domain denoising method for the flame image of the rotary kiln as claimed in claim 2, wherein: in the step S2, the specific steps are as follows: an adjacent matrix W constructed in the formula (1) i,j W, the degree matrix corresponding to the adjacent matrix W is D, and the constructed adjacent matrix W is used i,j The laplacian matrix L is constructed as:
L:＝D-W (2)，
the diagonal elements of the degree matrix D are the rows corresponding to the adjacency matrix W and are:
4. the frequency domain denoising method for the flame image of the rotary kiln as claimed in claim 3, wherein: in the step S3, the specific steps are as follows: performing first-level image wavelet decomposition on the rotary kiln flame image I and obtaining a coefficient matrix A of wavelets by Chebyshev polynomial approximation, wherein the dimension is Q 2 And (J +1), wherein the scale degree of the wavelet decomposition of the graph is J, the first column of the coefficient matrix A is a low-frequency coefficient, and the rest J columns are high-frequency coefficients with corresponding scales respectively.
5. The frequency domain denoising method for the flame image of the rotary kiln as claimed in claim 4, wherein: in the step S4, the specific steps are as follows: a first scale high frequency coefficient A [2 ] obtained by wavelet decomposition of the first level graph]∈R Q×1 Constructing an image matrix with m × n dimensions, and performing second-level image wavelet decomposition on the image to obtain a coefficient matrix B of second-level image wavelet transform with a dimension Q 2 And (J +1), wherein the scale degree of the wavelet decomposition of the graph is J, the first column of the coefficient matrix B is a low-frequency coefficient, and the rest J columns are high-frequency coefficients with corresponding scales respectively.
6. The frequency domain denoising method for the flame image of the rotary kiln as claimed in claim 5, wherein: in the step S5, the specific steps are as follows: the first scale high frequency coefficient B2 obtained by wavelet decomposition of the second level image]∈R Q×1 Constructing an image matrix with m × n dimensions, and performing a third-level image wavelet decomposition on the image to obtain a coefficient matrix C of the third-level image wavelet transform, wherein the dimension is Q 2 And (J +1), wherein the scale degree of the wavelet decomposition of the graph is J, the first column of the coefficient matrix C is a low-frequency coefficient, and the rest J columns are high-frequency coefficients with corresponding scales respectively.
7. The frequency domain denoising method for the flame image of the rotary kiln as claimed in claim 6, wherein: in the step S6, the specific steps are as follows:
s61: low-frequency coefficient B [1 ] obtained by wavelet decomposition of second-level image]∈R Q×1 And low-frequency coefficient C1 obtained by wavelet decomposition of third-level graph]∈R Q×1 Respectively reconstructed into m × n dimensional matrices B 0 [1]∈R m×n And C 0 [1]∈R m×n ；
S62: for matrix B 0 [1]∈R m×n And C 0 [1]∈R m×n And (3) carrying out non-local mean filtering: in wavelet coefficient matrix B 0 [1]∈R m ×n And C 0 [1]∈R m×n Selecting a point i, establishing a D multiplied by D noise search frame Z by taking the selected point i as a center, and taking a neighborhood frame with the size of D multiplied by D in the selected search frame, wherein a neighborhood window is positioned in a search windowSliding in the mouth; let the neighborhood vector composed of all wavelet coefficients in the neighborhood frame with the pixel point i as the center be v i And the neighborhood vector formed by all wavelet coefficients in the neighborhood frame with the pixel point j as the center is v j If the smoothing parameter is h, the similarity between two neighborhood windows is calculated to obtain the weight value U of the point j to the point i i,j Comprises the following steps:
8. the frequency domain denoising method for the flame image of the rotary kiln as claimed in claim 7, wherein: in the step S7, the specific steps are as follows:
s71: reconstructing the dimensionality of the coefficient matrix subjected to the non-local mean filtering and obtained in the step S6 to obtain a coefficient vector B consistent with the Chebyshev polynomial approximation dimensionality nlm [1]∈R Q×1 And C nlm [1]∈R Q×1 ；
S72: three low-frequency coefficients obtained by wavelet decomposition of the three-level graph are reconstructed:
Y[1]＝A[1] (5)，
Y[2]＝B nlm [1] (6)，
Y[3]＝C nlm [1] (7)，
obtaining a coefficient matrix Y ∈ R Q×(j+1) ：
When i > 3, Y [ i ]]＝0∈R Q×1 (8)，
Setting the operator matrix as G, and performing inverse transformation on the image wavelet coefficient Y to obtain a denoised rotary kiln flame image P as follows:
(G * G)P＝G * Y (9)。
9. a computer storage medium, characterized in that: stored therein is a computer program executable by a computer processor, the computer program executing a frequency domain denoising method of a flame image of a rotary kiln according to any one of claims 1 to 8.
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| CN109242799B (en) * | 2018-09-19 | 2021-10-12 | 安徽理工大学 | Variable-threshold wavelet denoising method |
| KR102216965B1 (en) * | 2019-05-07 | 2021-02-18 | 주식회사 힐세리온 | Noise removal apparatus and remote medical-diagnosis system using the same for removing noise from noisy image using discrete wavelet transform |
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